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# tile and bug problem

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A rectangular floor that is 10 feet wide and 17 feet long is tiled with 170 one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?

Feb 9, 2019

#1
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Use Pythagoras's Theorem:

Bug's Path^2 =10^2 + 17^2

=100 + 289

=389

=sqrt(389)

=19.72 - or ~20 tiles that the Bug crosses.

Feb 9, 2019
#2
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Thank you, but the answer is one of the following: 25,26,27,28

youchunhui  Feb 9, 2019
#3
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The following diagram should help:

Note that the equation of the diagonal line is $$y=\frac{10}{17}x$$  As x goes in integer steps from 0 to 17, y only takes integer values at x=0 and x=17.

Feb 9, 2019
edited by Alan  Feb 9, 2019